Details

sample179.0ms

Algorithm

intervals

Results

110.0ms	124×	body	1280	valid
41.0ms	71×	body	640	valid
8.0ms	26×	body	320	valid
3.0ms	11×	body	160	valid
2.0ms	24×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	23	12
2	23	12

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.3b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
1.6b	(cos (- lambda1 lambda2))
1.9b	(sin (- lambda1 lambda2))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

3×	`cos-diff`
2×	`sub-neg` `cos-sum` `associate-+r+` `sin-sum`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sin-diff` `flip-+`

Counts

4 → 11

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0ms	(cos (- lambda1 lambda2))
3.0ms	(sin (- lambda1 lambda2))

series153.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
99.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

simplify90.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	152	164
1	378	157
2	1080	154
3	2896	153
4	5002	153

prune91.0ms

Filtered

23 candidates to 14 candidates (60.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	17	6	23
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	18	6	24

Merged error: 1.1b

Counts

24 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
1.6b	(cos (- lambda1 lambda2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

3×	`+-commutative` `distribute-rgt-in` `cos-diff` `distribute-lft-in`
2×	`cos-sum` `associate-+r+` `flip3-+` `associate-*r/` `flip-+`
1×	`sub-neg` `*-commutative`

Counts

4 → 15

Calls

4 calls:

8.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
1.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0ms	(cos (- lambda1 lambda2))

series278.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
13.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
101.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))

simplify49.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	207	247
1	574	240
2	1766	238
3	5001	237

prune123.0ms

Filtered

27 candidates to 18 candidates (66.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	24	3	27
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	28	5	33

Merged error: 0.2b

Counts

33 → 5

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
0.5b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate-+r+`
10×	`*-commutative`
8×	`distribute-rgt-in` `distribute-lft-in` `prod-diff`
3×	`+-commutative`
2×	`sub-neg` `flip3-+` `associate-*r/` `flip-+`
1×	`sin-neg` `distribute-rgt-neg-out` `sin-mult`

Counts

4 → 25

Calls

4 calls:

8.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
4.0ms	(* (sin lambda1) (sin (- lambda2)))
1.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
8.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
53.0ms	(* (sin lambda1) (sin (- lambda2)))
18.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
225.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	270	420
1	681	405
2	2450	396
3	5003	395

prune162.0ms

Filtered

37 candidates to 24 candidates (64.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	4	0	4
Picked	0	1	1
Done	0	0	0
Total	38	4	42

Merged error: 0.2b

Counts

42 → 4

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
0.4b	(pow (cos phi1) 3)
0.6b	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
1.1b	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate--l+`
10×	`*-commutative`
8×	`prod-diff`
6×	`distribute-rgt-in` `distribute-lft-in`
3×	`sub-neg` `unpow3` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `fma-def` `fma-neg`
1×	`+-commutative` `flip3--` `flip3-+` `sum-cubes` `flip--` `flip-+`

Counts

4 → 32

Calls

4 calls:

9.0ms	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
1.0ms	(pow (cos phi1) 3)
5.0ms	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
13.0ms	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.1s	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
27.0ms	(pow (cos phi1) 3)
199.0ms	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
213.0ms	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

simplify47.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	463	620
1	1739	607
2	5001	577

prune333.0ms

Filtered

44 candidates to 35 candidates (79.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	40	4	44
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	41	7	48

Merged error: 0.2b

Counts

48 → 7

regimes386.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	24
1	31	24

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.3s	3653×	body	1280	valid
1.2s	2318×	body	640	valid
322.0ms	903×	body	320	valid
95.0ms	406×	body	160	valid
74.0ms	720×	body	80	valid